Phase Analysis for a family of Stochastic Reaction-Diffusion Equations

Abstract: We consider a family of stochastic reaction-diffusion equations driven by space-time white noise. The reaction term belongs to a large family of functions that includes Fisher-KPP nonlinearities [V (x) = x(1 − x)] as well as Allen-Cahn potentials [V (x) = x(1 − x)(1 + x)] . We show that (i) if the noise intensity is large, our stochastic PDE has the unique invariant measure; and (ii) if the noise intensity is small, the collection of all invariant measures is a non-trivial line segment, in particular infinite. Our methods also say a great deal about the structure of these invariant measures. This is based on joint work with Davar Khoshnevisan, Carl Mueller and Shang-Yuan Shiu.

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html